Polarized proton elastic scattering and Nucleon density distributions · 2018. 11. 16. · Elastic Scattering of Protons with RI beams (ESPRI) project RCNP I.Tanihata H.Jin Ong GSI

Polarized proton elastic scattering and Nucleon density distributions

Juzo Zenihiro, RIKEN Nishina Center

outline

1. Nucleon density distributions

2. Polarized proton elastic scattering

3. How to extract

4. Effective NN interaction

5. Extraction of rn(r)

6. New method of simultaneous extraction of rp(r), rn(r)

7. Summary and future perspective

2014/10/24 SPIN2014 2

Point-nucleon density distributions

Fundamental information of nuclei; rp(r),rn(r) Nuclear size & shape are helpful for comprehensive

understanding of nuclear structure & reaction model,

Neutron skin thickness the nuclear matter EOS

Stable nuclei • Proton density distribution rp(r) : derived from rch(r)

– Charge distribution rch(r) : EM probe (simple )

– For example, rch = 208Pb : 5.5010(9) fm (0.02% accuracy)

• Neutron density distribution rn(r) : Our work – Hadronic probe (very complicated)

– Suffering from large uncertainties

Incomplete knowledge of NN interaction inside nucleus

Unstable nuclei • Little information about rp(r), rn(r), rch(r) !

Investigate a new method of simultaneous extraction of rp(r), rn(r) : Our work

3 2014/10/24

I. Sick et al, PRL35(75)910, NPA218(74)509

58Ni(e, e) elastic

H. de Vries, et al, ADANDT36, 495, and so on.

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2014/10/24 SPIN2014 4

+Ze

N+Z

e- e-

P↑

Electron scattering

Proton scattering

@ 300 MeV

g

?? meson

)()()(

)()(

rqFqF

rqF

pp

p

ch

A

ch

A

ch

r

r

)()( rqF npnp r

)(),( rr np rr

; Nuclear charge

; Nuclear matter

MottddA

chdd qF

2

)(

pnnp rrr

: well established in 1980s

: our work

Polarized proton elastic scattering

P↑

2014/10/24

Ring cyclotron facility @RCNP

polarized

proton beam

scattering

chamber

VDCs & plastic

scintillators

GR LAS

West experimental

Hall

5

2 cyclotrons in a coupled

mode : AVF (53 MeV) and

Ring (295 MeV) cyclotron

WS beam line in West Exp.

Hall

Vertically polarized proton

beam at Ep = 295 MeV

Achromatic transport on

target. Spot size : ~ 1mm-j

Experimental conditions Scattering observables :

d/d, Ay, Q Beam energy : 295MeV Beam polarization : 70~80% Energy resolution : <200keV Angular & momentum

transfer range : 8~50deg., 0.5~3.5fm-1

Target : 40-48Ca, 58Ni, 90,92,94Zr, 116-124Sn, 204-208Pb

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How to extract neutron densities from proton elastic scattering?

RIA (tr optical potential)

Effective NN interaction

Nucleon density distribution :

rpV(r), rn

V(r), rpS(r), rn

S(r)

+

ds/d, Ay, Q ds/d, Ay, Q

Experimental data Calculation

input

output

c2 method

Modify the RLF interaction

to explain real data (58Ni)

Fixed

rpV(r) : unfolding rch(r)

rS = 0.96 rV

Free parameter

rnV(r) : minimize the c2

2014/10/24 6

folding

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C. J. Horowitz, PRC31, 1340(1985). D. P. Murdock et al., PRC35, 1442(1987).

.,

/1

,/1

rr

rr

j

rbmmm

ra

ggg

jjjj

j

2

j2

j

2

j

Effective NN interaction

2014/10/24 7

Medium effect

H. Sakaguchi et al., PRC57, 1749. S. Terashima et al., PRC77, 024317.

NN interaction

Universal form of density-

dependent terms

At r=0, same as free NN

interaction

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Medium modification of RLF NN interaction

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Calibration of medium effect by 58Ni Four free parameters: aj, bj

(j=, )

rp(r) : unfolding rch(r)

rn(r) = (N/Z)rp(r)

j

aj -0.044(26) 0.037(40)

bj 0.097(13) 0.075(21)

minimum c2

search

c2min/n~10.

calcexp

calcexp200

d

Differential cross sections & analyzing powers of

300 MeV polarized p-58Ni elastic scattering

Calibrated medium effect parameters

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Extraction of neutron densities of Pb isotopes

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Fixed medium effect parameters

by 58Ni data: aj, bj (j=, )

rp(r) : unfolding rch(r)

rn(r) : SOG model independent

function

proton elastic scattering from 204,206,208Pb

minimum c2

search

1 ,)/21(2

,)()(

2232/3

/)(/)(SOG 222

i

i

ii

RirRir

in

QR

NQA

eeAr

gg

γγ２ρ

Fixed : g, Ri (same as rch(r))

Free parameters : Qi (i=1~12)

reduced c2min ~ 4.

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Error-envelope of rn(r)

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208Pb case

rn type c2/n (n=47) rn (fm)

3pG 255/47=5.4 5.593

SOG 192/47=4.1 5.653(30)stat.

Error-envelopes due to exp. errors :

c2 ≦ c2min + c2.

Comparison with previous rn(r) :

3-parameter-Gaussian (3pG) by L.

Ray (Ref.[58])

~11

0.06 fm

(1%)

percent deviation

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Polarized proton elastic scattering at 300MeV (Ring cyclotron facility at RCNP, Osaka University)

⇒We have succeeded in extracting neutron density distributions of Sn, Pb isotopes systematically.

S.Terashima et al.,

Phys. Rev. C 77,

024317 (2008)

J.Zenihiro et al.,

Phys. Rev. C 82,

044611 (2010)

Sn

Pb

Stable nuclei : rp is known. d/d, Ay rn(r) rnp

RIA

+

Medium

modification

rn/rn < 0.5%

Extraction of rn(r)

2014/10/24 SPIN2014 11

2014/3/5 WS @ kyushu-u 12

+Ze

N+Z

e- e-

p p

Electron scattering

Proton scattering

@ 300 MeV

g

meson

)()()(

)()(

rqFqF

rqF

pp

p

ch

A

ch

A

ch

r

r

)()( rqF npnp r

)(),( rr np rr

; Nuclear charge

; Nuclear matter

MottddA

chdd qF

2

)(

pnnp rrr

: well established in 1980s

: our work

For stable nuclei

Simultaneous extraction from two-energy p-elastic data

2014/10/24 SPIN2014 13

N+Z

p p

Proton scattering

@200MeV

Proton scattering

@ 300 MeV

meson

)(),( rr np rr pnnp rrr

For unstable nuclei

N+Z

p p

meson )()()()( 200200 rrqFtqFt npnpnppp rr

)()()()( 300300 rrqFtqFt npnpnppp rr

Simultaneous extraction from two-energy p-elastic data

Energy dependence of NN interaction and Nuclear potential

Expecting…

1. pp & pn interactions are different and have different energy-dependences from each other.

2. Central part of nuclear optical potential changes shallow attractive to shallow repulsive from 200 to 300 MeV (-5 ~ 10 MeV), while the nuclear Coulomb potential does not change and relatively large (> 10 MeV)

Scattering observables are really sensitive to both densities?

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Central part (Vc) of optical potentials

Test experiment at RCNP (E366)

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Obtained data of 90Zr, 58Ni

@ 200, 300 MeV Blue : original RIA

Red : RIA with realistic rp

& rn =rp *N/Z

Calibrate effective NN

interaction @ 200MeV

For 300MeV already

calibrated by previous

work ↓

J.Zenihiro et al.,Phys. Rev. C

82, 044611 (2010)

Some results

2014/10/24 SPIN2014 16

Fitting results for 90Zr @ 200 & 300 MeV

Simultaneous search of Neutron & Proton

From 300 & 200 MeV data

rn rp rnp

4.300(17) 4.210(20) 0.090(26)

Extracted densities of 90Zr

Summary

• For stable nuclei – We developed a new description of effective interaction in the

framework of RIA, and which is very successful. – Proton density distributions can be derived from nuclear charge

distributions – We succeeded in extracting rn(r) of Pb, Sn isotopes from

polarized proton elastic scattering

• For unstable nuclei

– New method has been developed to extract both rp(r), rn(r) from two-energy proton elastic scattering data.

– Feasibility test experiment has been done and the preliminary result shows that this method works very well!

2014/10/24 SPIN2014 17

Ongoing & future

• ESPRI project (Elastic Scattering of Protons with RI beam) has been already launched. – Detector development and test using RI beam has been done at

HIMAC, Chiba and GSI, Germany. – 1mm-t & 30mm-f pSHT [Y. Matsuda, et al., NIMA643, 6(2011)] – Excitation energy resolution ~ 500 keV()

• ESPRI experiments @RIBF, RIKEN, Japan

– NP0709-RIBF40 : 16C at 300MeV/u (light unstable nuclei) Successfully done in FY2013!

– NP1112-RIBF79 : 132Sn at 200&300MeV/u Approved. • Experiment will be performed in FY2015 • The new method will be adopted. • neutron skin thickness of 132Sn will constrains the symmetry energy.

2014/10/24 SPIN2014 18

4. ESPRI detectors

2014/3/5 WS @ kyushu-u 19

Drift Chamber

Plastic scintillator

Solid hydrogen

target

θlab = 66° - 80°, Ep=20-120 MeV, ΔΩ〜10 msr/deg.

q=1-2.2 fm-1, ΔEx = 400-500 keV

Recoil drift chamber 436x436 mm2 (x-y-x’-y’-x’-y)

Plastic scintillator 440x440 mm2 x 2 mmt

NaI(Tl) calorimeter 431.8x45.72 mm2 x 50.8 mmt

1 mmt

φ30 mm

Recoil Proton Spectrometer (RPS)

Elastic Scattering of Protons with RI beams (ESPRI) project

RCNP

I.Tanihata

H.Jin Ong

GSI

S272 collaborators

NIRS

E.Takada

M.Kanazawa

RIKEN

H.Takeda

K.Ozeki

K.Yoneda

Tohoku Univ.

T.Kobayashi

Kyoto Univ.

T.Kawabata

T.Murakami

M.Tsumura

T.Furuno

Miyazaki Univ.

Y.Maeda

Collaborators

S.Terashima (Beihang Univ.)

Y.Matsuda (RCNP)

H.Sakaguchi (RCNP)

H.Otsu (RIKEN)

T.Baba (Kyoto Univ.)

2014/10/24 SPIN2014 20

Thank you!

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2014/10/24 SPIN2014 22

2014/10/24 SPIN2014 23

protons & neutrons in a nucleus

2014/10/24 SPIN2014 24

How are nucleons (p, n) distributed in a nucleus? : rp, rn

Nucleus is finite quantum many-body system made from 2 different fermions, p & n.

fundamental and direct information to constrain nuclear structure or reaction models

Shell structure Saturation property Halo, skin structure nuclear matter

EOS with isospin asymmetry

Neutron skin thickness vs. Symmetry energy

pp total cross section

np total cross section

Good probe to extract interior information of nucleus

– Interact with both neutrons and protons

– long mean free path (~2fm)

interior structure ( surface structure)

– one-step reaction is dominant

simple description ; successful Relativistic Impulse Approximation (RIA)

25

300 MeV proton

2014/10/24 SPIN2014

RIA framework • Dirac tr-optical potential : single folding

of NN amplitude (t) & densities (r) – NN amplitude; 10 mesons’ coupling

including both direct & exchange terms are tuned by free NN phase shift analysis(RLF model by C. J. Horowitz)

– For spin-0 nucleus only Scalar & Vector component remain

Relatively good agreement with p-A scattering data, particularly, analyzing powers above 100 MeV

• Not enough to extract densities Need effective NN interaction inside

nuclear medium

2014/10/24 SPIN2014 26

D. P. Murdock and C. J. Horowitz, PRC35, 1442. C. J. Horowitz and B. D. Serot, NPA368, 503. H. Sakaguchi et al., PRC57, 1749.

Calibration of medium effect by 58Ni

58Ni

58Ni

58Ni

size same almost the : pn rr

Various experimental & theoretical

results say :

)()( rZ

Nr pn rr

2014/10/24 27 SPIN2014

58Ni rp rn rnp Ref.

DME+D1 3.68 3.67 -0.01 PRC21, 1568(1980)

HF-BCS+SIII 3.738 3.732 -0.006 NPA603, 23(1996)

HF-BCS+SkM* 3.722 3.720 -0.002 PRC33, 335(1986)

HF-BCS+SGII 3.719 3.697 -0.012 PRC72, 044307(05)

RMF+NL3 3.652 3.691 0.040 ADNDT71, 1(1999)

RMH+RH 3.652 3.691 0.039 NPA368, 503(1981)

Glauber 3.763(50) 3.72(5) -0.043(70) PLB67, 402(1977)

Glauber 3.67(5) 3.60(5) -0.07(7) PLB72, 33(1977)

Glauber 3.763(50) 3.75(10) -0.01(7) NPA360, 233(1981)

1st KMT 3.688 3.652(74) -0.035(74) PRC18, 2641(1978)

2nd KMT 3.686 3.700(50) 0.014(50) PRC19, 1855(1979)

p atom - - -0.09+0.09-0.16 PRL87, 082501(01)

This work 3.680 3.680 0.000

2014/10/24 28 SPIN2014

)./(

~~

2

min

22

min

22

min

2

22

min

2

nccc

ccc

ccc

S

2014/10/24 29

Estimation of error-envelopes of rn(r)

c2min/n ~ 4 : incompleteness of the

theoretical model as well as

unknown experimental systematics

Error-envelopes due to model

uncertainties :

S realizes c2min/n 1.

.~

,~

2

min2

2

min2

min

2

exp

calcexp

2

22

nc

nc

c

cc

SS

yS

yy

S

Total error-envelope SPIN2014

Neutron root-mean-square radii

2014/10/24 30

rch rpunfold rn rn

std rnmdl

204Pb 5.479(2) 5.420(2) 5.598 +0.029 +0.047

-0.020 -0.059

206Pb 5.490(2) 5.433(2) 5.613 +0.026 +0.048

-0.026 -0.064

208Pb 5.503(2) 5.442(2) 5.653 +0.026 +0.054

-0.029 -0.063

Extracted rn, rn

2 types of errors of rn : due to

experimental errors only (rnstd) ~ 0.5 %

total errors including model &

unknown systematic uncertainties (rnmdl) ~1 %

(all in fm)

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2014/10/24 31

The symmetry energy coefficients

deduced from rnp for 204,206,208Pb

Deduced region of the symmetry

energy coefficients : weighted average

S(rsat) = 33.0±1.1 MeV

L = 67.0±12.1 MeV

comparable with previous studies

but still large

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!!Note that 3 ranges in plot are

due to experimental errors only!!

2014/10/24 SPIN2014 32

proton neutron

r/r ~ 0.35%

Simulation results of simultaneous

extraction of rp(r), rn(r)

r/r ~ 0.8%

208Pb

Z=82

14C

Z=6

Simulation results from pseudo-data (ds/d, Ay) of 208Pb, 14C(p,p) at

200, 300 MeV with ~5% experimental errors.

Error envelope from 5% exp. errors

Best fit (solid)

Input (dashed)

1 ,)/21(2

,)()(

2232/3

/)(/)(SOG 222

i

i

ii

RirRir

in

QR

NQA

eeAr

gg

γγ２ρFixed : g, Ri (same as rch(r))

Free parameters : Qi (i=1~12)

The case of unstable nucleus; 132Sn

2014/10/24 SPIN2014 33

Test of simultaneous extraction of rp(r), rn(r) of 132Sn from pseudo-

data of differential cross sections

132Sn

g.s. (input) g.s. (extracted) r/r

rn 4.916 4.907(23) 0.46%

rp 4.650 4.612(49) 1.0%

rnp 0.266 0.295(54) --

Using RIA and relativistic-Hartree

calculations as nucleon density

distributions.

2014/10/24 SPIN2014 34

Extraction of densities of 90Zr

Fitting results for 90Zr Search rn of 90Zr only

From 300MeV

From 200MeV

Radius (fm)

Very preliminary !!

Simultaneous search of Neutron & Proton

From 300 & 200 MeV data

Neutron 300MeV 200MeV both

Proton

Comparison of 3 ways

Extracted radii and skin of 90Zr

2014/10/24 SPIN2014 35

Type I Type II Type III

c2/n 262/45 218/53 488/98

rn 4.285(16) 4.300(22) 4.300(17)

rp 4.200 4.200 4.21(2)

rnp 0.085(16) 0.100(22) 0.090(26)

Type I : 300MeV data only

Type II : 200 MeV data only

Type III : 200 & 300 MeV data

* Errors are experimental only!

(all in fm)

Very preliminary !!

Recoil proton spectrometer (RPS)

2014/10/24 SPIN2014 36

RI

[Photo]

ESPRI measurement for 16C

2014/10/24 SPIN2014 37

NaI(Tl) ADC

Pla

stic (

pd

E)

QD

C

Plastic TDC

dE-TOF dE-E

16C beam profile on SHT

Clear identification of recoil protons

[Data]

SH(16C, p)*C

Recoil proton angle [degree] R

ecoil

pro

ton e

nerg

y [

MeV

]

Kinematical correlation plot

elastic

inelastic

Analysis is ongoing.

Summary 1. ESPRI @ HIMAC, Chiba and GSI, Germany. Successfully done!

HIMAC-P179&P213 : 9C, 10,11C, 20O (FY2007-2009) [Y. Matsuda, et al., Phys. Rev. C87, 034614(2013)]

GSI-S272 : 66,70Ni (FY2009-2010)

1mm-t & 30mm-f pSHT [Y. Matsuda, et al.,NIMA643,6(2011)], energy resolution of ~500keV()

still large experimental errors due to low statistics

2. Test of the simultaneous extraction of rp(r) & rn(r) from proton elastic scattering data at 200, 300 MeV/u two-energy analysis method is now being developed with stable nuclei.

RCNP-E366 : 90,92,94Zr (FY2012)

RCNP-E375 : 12,13,14C (FY2013-2014)

feasibility test experiment (E366) shows good results.

3. ESPRI @ RIBF with high-intensity RI beam NP0709-RIBF40 : 16C at 300 MeV/u (light unstable nuclei; successfully done in April 2013!)

NP1112-RIBF79 : 132Sn at 200&300 MeV/u (heavy unstable nuclei; approved by 2011 NP-PAC) Detectors are now being developed.

Will be performed in 2015 (14 days).

4. Stable nuclei Neutron densities of Sn & Pb isotopes, neutron skin of 208Pb

Neutron skin of 48Ca, 90Zr

5. Future work? HI+HI elastic scattering r~ 2r0 : T. Furumoto, et. al,. PRC85,044607(2012)

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